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A096379 a(n) = prime(n) + prime(n+1) - prime(n+2). 7
0, 1, 1, 5, 7, 11, 13, 13, 21, 23, 27, 35, 37, 37, 41, 51, 53, 57, 65, 65, 69, 73, 75, 85, 95, 97, 101, 103, 95, 109, 121, 129, 127, 137, 143, 145, 153, 157, 161, 171, 169, 179, 187, 191, 185, 187, 207, 221, 223, 223, 231, 229, 235, 245, 251, 261, 263, 267, 275, 271 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

Sequence is non-monotonic: see, e.g., a(29), a(33), and a(41). - Zak Seidov, Jan 21 2013

Ishikawa proved that a(n) > 0 for n > 1. - Jonathan Sondow, Feb 13 2014

LINKS

Michel Marcus, Table of n, a(n) for n = 1..5000 (terms 1..1000 from Zak Seidov)

Heihachiro Ishikawa, Über die Verteilung der Primzahlen, Sci. Rep. Tokyo Bunrika Daigaku, Sect. A 2 (1934), 27-40.

FORMULA

a(n) = A001043(n) - A000040(n+2). - A.H.M. Smeets, Aug 17 2019

a(n) = A000040(n) - A001223(n+1). - Jon Maiga, Aug 17 2019

EXAMPLE

a(1) = prime(1) + prime(2) - prime(3) = 2 + 3 - 5 = 0.

a(25) = prime(25) + prime(26) - prime(27) = 97 + 101 - 103 = 95.

MAPLE

A096379 := proc(n)

    ithprime(n+1)+ithprime(n)-ithprime(n+2) ;

end proc:

seq(A096379(n), n=1..80) ; # R. J. Mathar, Sep 10 2016

MATHEMATICA

#[[1]] + #[[2]] - #[[3]] & /@ Partition[Prime[Range[62]], 3, 1] (* Zak Seidov, Apr 09 2013 *)

ListConvolve[{-1, 1, 1}, Prime[Range[100]]] (* Zak Seidov, Dec 03 2014 *)

PROG

(PARI) g(n)=for(x=1, n, print1(prime(x)+prime(x+1)-prime(x+2)", "))

(PARI) first(n)=my(v=vector(n), p=2, q=3, k); forprime(r=5, , if(k++>n, break); v[k]=p+q-r; p=q; q=r); v \\ Charles R Greathouse IV, Oct 03 2017

(MAGMA) [NthPrime(n)+NthPrime(n+1)-NthPrime(n+2):n in [1..60]]; //  Marius A. Burtea, Aug 17 2019

CROSSREFS

Cf. A000040, A001043, A001223.

Sequence in context: A136162 A054500 A082684 * A098761 A113837 A255363

Adjacent sequences:  A096376 A096377 A096378 * A096380 A096381 A096382

KEYWORD

nonn,easy

AUTHOR

Cino Hilliard, Aug 04 2004

EXTENSIONS

Edited by Zak Seidov, Aug 27 2012

Definition reworded by N. J. A. Sloane, Aug 27 2012

STATUS

approved

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Last modified January 17 14:39 EST 2022. Contains 350401 sequences. (Running on oeis4.)